Monocular information plays a crucial role in depth perception (e.g. da Vinci stereopsis1). Despite some explanatory successes, many popular physiological models of depth perception, such as the disparity energy model2, do not incorporate monocular information and so are limited to describing stereopsis. The present work goes beyond these models by developing a detailed laminar cortical theory of how monocular and binocular information interact in areas V1, V2 and V4 of the macaque visual cortex to form coherent percepts of depth with particular emphasis on surface depth perception. This model builds on previous work that links cortical circuits to psychological and neurophysiological data about grouping, attention and development3. It is consistent with the disparity energy model but makes novel predictions. In particular it provides neural explanations for psychophysical data including: contrast variations of Panum's limiting case and dichoptic masking, depth perception of monocularly viewed objects, da Vinci stereopsis and various lightness illusions, thereby linking known laminar cortical anatomy and physiology to psychophysics and providing new functional insights and predictions about cortical architecture. A psychophysical study has recently found supporting evidence for the model's explanation of the depth perception induced by opposite contrast stereograms by showing that, contrary to several published claims, stereopsis can be achieved only by the binocular fusion of edges whose luminance gradients have the same-sign.